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Finite - Definition and Overview |
| Related Words: Algorithmic, Anthropocentric, Anthropological, Bound, Bounded, Cardinal, Conditioned, Copyrighted, Countable, Decimal, Definable, Defined, Delimited, Differential, Digital, Even, Exponential |
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In mathematics, a set is called finite if and only if
there is a bijection between the set and some set of the form {1, 2, ..., n} where <math>n<math> is a natural number. It is a theorem that a set is finite if and only if there exists no bijection between the set and any of its proper subsets. Equivalently, a set is finite if its cardinality, i.e. the number of its elements, is a natural number. For instance, the set of integers between -15 and 3 is finite, since it has 17 elements. The set of all prime numbers is not finite. Sets that are not finite are called infinite.
In physics, finite additionally means "non-zero", for instance in a sentence like "if the distance of the two objects is finite...".
See also: infinity, countable set
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